It’s only been a few days since American Apparel was rescued from the threat of Chapter 11, but CEO Dov Charney is already talking big again.

The famously randy founder of the Los Angeles-based clothing chain — who lately has been fighting off a string of lurid sex-harassment lawsuits from ex-employees — says his company is now gunning for a turnaround to match the greats in the annals of US business.

“People didn’t believe in Amazon for many years, but it ended up changing the way Americans shop,” Charney told The Post in an interview yesterday, likening his company to the e-commerce giant that was savaged by media and investors a decade earlier as it battled debts and accounting questions.

“People didn’t believe in Apple — they thought it was a fringe computer company,” Charney added. “But it ended up changing the way people listen to music, and changing what daily life feels like worldwide.”

Charney’s own plans to revolutionize the US clothing industry — which include ramping up production at the company’s Los Angeles factory following a crippling immigration bust in 2009 — got a helping hand last week. As reported by The Post, a coterie of Canadian investors agreed to inject as much as $43 million into cash-strapped American Apparel.

Led by Michael Serruya, a frozen-foods tycoon who in 2009 made a bundle bailing out Jamba Juice, the Great White North investors injected $15 million into American Apparel immediately. During the next six months, they’ll get the option to buy nearly a third of the company at just 90 cents a share — a 27-percent discount to last week’s closing price.

The deal looked like a daredevil move to some critics, who charge that Charney has blown through $80 million during the past years with a haphazard, control-freak management style.

But in addition to its strong support of Charney as top executive, the Canadian contingent sees huge potential in American Apparel’s manufacturing and distribution facilities in LA, according to Roy Sebag of Essentia Equity, one of the firms participating in the bailout.

“If there ever was a time it made sense to produce apparel in the US, it’s now,” Sebag told The Post, citing the decline of the US dollar, the rise of Chinese wages and transportation costs, and a growing craze for fast fashions.

“The US cannot become an economy that depends on outsourced manufacturing and outsourced labor — long-term, it doesn’t work.”

Sources said American Apparel’s LA factory has recovered about two-thirds of the efficiency it lost after the immigration bust, which is estimated to have siphoned away as much as $50 million of the company’s cash last year in lost sales and squeezed margins.

Sources said the LA facilities have the capacity to support as much as $1 billion in company sales — nearly double their current levels. james.covert@nypost.com